On an exam:
— Find the sum of the k-th degrees of the first N positive integers.
— That's easy. What's N?
— N is unknown, solve the problem in the general case.
— So how can I find this sum if N is unknown?
— We discussed it at the lectures. The sum 1^k + 2^k + 3^k + … + N^k for any k is a polynomial P(N) of degree k+1 with rational coefficients. For example, 1 + … + N = N(N+1)/2. Given k, find the coefficients of this polynomial.

Can you solve this problem?

An integer 0 ≤ k ≤ 30.

Output coefficients of the polynomial P(N) = A_k+1N^k+1 + A_kN^k + … +A₁N + A₀ in the form of k+2 irreducible fractions. A fraction has the form "a/b" or "−a/b", where a and b are integers, b ≥ 1, a ≥ 0. The coefficients must be given in the order of descending degrees (from A_k+1 to A₀). It is not allowed to omit denominators of the fractions or leave out zero coefficients. Separate the fractions with a space.